VOL. 41, NO. 3 (SEPTEMBER 1988) P. 236-238 The Spiral in the of the Narwhal MICHAEL C.S. KINGSLEY’ and MALCOLMA. RAMSAY ’**

(Received 2 December 1987; acceptedin revised form10 May 1988)

ABSTRACT. The spiral in the tusk of the narwhal has been fancifully, but never satisfactorily, explained.Spiral growths are common in the kingdom and share the feature of having straight axes. A curved tusk would hinder the narwhal swimming; a spiral mode of growth ensures overall straightness even if the tusk grows irregularly. The need to keepthe tusk straight completely and satisfactorily explainsthe spiral. Key words: Monodon monoceros, , morphology, asymmetry

RÉSUMÉ.On a explique le fait que la come du narval soit spiralte de manitre originale mais jamais satisfaisante.Les croissances en spirale sont un phénombne commun dansle &gne animal etelles posstdent toutesla caracttristique d’avoir des axes rectilignes. come Une incurvte gênerait la nagedu narval; une croissance s~iraléeassure Que l’ensemble est rectiligne même si la come pousse de façonMgulière. La ntcessitt pour la come de pousser droit justifie entièremedt et elle seule le phtnomtne de la spiale. Mots clés: Monodon monoceros, dentition, morphologie, asymttrie Traduit pour le journal par Ntsida Loyer.

The tusk of the narwhal(Monodon monoceros) is remarkablein 1942; Ness, 1978; and see, for example, Tafel 17 in Pilleri, several ways: it is unique among the ; it is straight; it 1983); so are other forwardprojections among aquatic , usually only develops on the left side; and when, rarely, both such as the spears and saws of the billfishes and sawfishes left and right develop, they both twist left-handed instead (Norman andFraser, 1937). If the tusk twists as it grows, each of mirroring each other (Thompson, 1942). Its phylogeny and point around the tuskpasses in turnover regions in the socket of function have aroused much discussion (Thompson, 1942; faster and slower growth, and any imbalance of growth rate Silverman and Dunbar, 1980; Best, 1981; Gerson and Hickie, around the tusk base isevened out; the result is a straight axis. 1985); we do not here add to that, but intend onlyto suggest a Spiral structures with straight axes are common in the animal reason for the conspicuous spiral. kingdom (Thompson, 1942; Illert, 1983), as horns, shells, teeth, Although almost every writer on narwhal has remarked that and tusks: “. . . the seashell, the elephant’s tusk, the beaver’s the tusk spirals, few have suggested why. The only reasoned , even the claws of a canary, all have in common the way in explanationfor the spiral wasgiven by D’ArcyThompson which theyare produced” (Illert, 1983: 22). They are those that, (1939, 1942), who thought that asymmetrical propulsion from likethe narwhal tusk, growat the base onlyand maintain the tail might cause it and suggested the same cause - asym- constancy of shape while growing. The exaggerated projecting metrical propulsion- for the asymmetry generalin the skullsof teeth of someother , such as the babiroussa (Bubyrousu odontocetes. This would explain why right-hand tusks should bubyrussu) and theelephants (Elephus maximus and Loxodontu break symmetry and twist the same way as left-hand. Pilleri ufricuna), are curved and maybe true spirals(Dow and Hollenberg, (1983) credited Thompson’s explanationfor the spiral so far as 1977); the anomalous lower-jaw narwhal tusk reported by Mitch- to measure the momentarm of the tail stock andflukes. We doubt ell and Kemper (1980) forms the first half-turn of a corkscrew this explanation. Neither author gave more than a heuristic spiral of 16 cm diameter. assessment of plausibility for it nor a rational mechanical expla- We suggest that a sufficient explanation, and the only one nation; Pilleri( 1983), after measuring the momentarm, presented needed, for the spiral in the narwhal’s tuskis that it ensures that no subsequent calculations of its effect. No one has developed the tusk will growstraight overall (Fig. l), even though therate Thompson’s hypothesis quantitatively, and other authors have of growth does vary, as the surface irregularity shows, greatly found no evidence for asymmetrical propulsion. The asymme- around the root(Fig 2). That right and lefttusks twist the same try in the skulls of odontocetes, developedrecently (Ness, way is then theoutcome of a 5050 chance: a twist ofeither hand 1967), is associated theirrefinedwith acoustic capabilities(Mead, would serve equally wellto keep the tusks symmetrically straight. 1975; Gaskin, 1982); mysticetes have symmetrical skulls. No rkcherchk asymmetry in swimming need be imagined; the The narwhal tusk isa tooth, and long teeth growby continued narwhal doesn’t corkscrew forwardthrough the water, leaving deposition at the root. Unless the rate of deposition of new its tusk in rotational arrears. The narwhal produces a massive material were perfectly balanced all aroundthe root, a curved display organ that it can tolerate in its aquatic existence, adapt- tusk wouldresult, and sucha long tusk, if curved, would hinder ing a common phenomenon as a mode of production that can the narwhal when swimming. One feature of narwhal tusks is insure the straightness of the tusk axis against congenital or that theyare overall almost perfectly straight(Thompson, 1939, traumatic aberrations.

~~~ ‘Freshwater Institute, Department of Fisheries and Oceans, Winnipeg, Manitoba, R3T2N6 *Present address: Departmentof Biology, The University of Saskatchewan, Saskatoon, Saskatchewan, CanadaS7N OW0 @The Arctic Instituteof North America NOTES I 237

FIG. I. Narwhal tusks are overallalmost perfectly straight . . . FIG. 2. . . . althoughthey may grow irregularly on a smaller scale. 238 I NOTES

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